Quantum Monte Carlo of cohesion and excitations in diamond Si: benchmarks

We present a study of Si bulk in diamond structure by fixed-node (FN) QMC since systems with Si tend to exhibit some of the smallest FN errors. This is due to the prevalence of single, spatially separated bonds as well as favorable spatial character and energetic ordering of the atomic levels. These features make it very convenient to study finite-size effects and scaling of both ground and excited states as the cell size is increased. This is carried out for HF and DFT sets of initial orbitals used in the construction of correlated wave functions in VMC and DMC. The cohesive energy is obtained very accurately, the FN error being ∼1% of the correlation energy that provides E_coh=4.629±0.08±0.002 eV where 1^st uncertainty is an estimated systematic error while 2^nd one is random error. The excitations Γ→Γ, and Γ→Χ are also studied using large cells of 64 and 216 atoms. We found that the thermodynamic limit (TDL) gaps can be reliably estimated using only these 2 data points with residual errors ≈0.2 eV. The bandgaps are found to be influenced by the orbital sets, and by the size and type of cells used. We emphasize the importance of reaching the TDL consistency as well as proper analysis in obtaining reliable estimates.